Section 1 Lab Activity-complete

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Statistics

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Apr 3, 2024

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STAT 3090 S ECTION 1 L AB A CTIVITY S PRING 2024 N AME : Matt Schmidt P URPOSE : Some of the first questions we need to ask ourselves when confronted with interpreting data are “Who or what is this data about?”, “Where did this data come from?”, What kind of data am I looking at?”. These initial questions will help us determine how to analyze and interpret the data. The following activity will help us practice answering these questions using the language specific to statistics. O BJECTIVES : Upon successful completion of this assignment, you will be able to…  Classify data into data types  Identify the population, sample, parameter, statistic in context  Determine if a statistic is being used for inference  Determine the type of study from the context of a problem  Distinguish between explanatory and response variables 1. Sleepy Hollow (40 pts) The town of Sleepy Hollow has 18,000 residents over the age of 10. We have recorded for us the number of hours generally slept per night by each resident over the age of 10. You will find this data by going to the website: https://www.rossmanchance.com/applets/2021/sampling/OneSample.html Be sure that the population data is for “Sleep 1”. Also, select “Show Sampling Options” on the right side. Realistically, it would be very difficult to record data for every person in this town. Thus, we would likely take a sample of the residents, calculate statistics from the sample data, and use those statistics as an educated guess for the actual population parameters of interest. We will use this data set to draw a sample of size 9 to illustrate several concepts of populations, samples and data. a. What is the population? (4 pts) 18,000 residents. b. Define at least two parameters that could be calculated from this population data. (4 pts) Population mean and standard deviation. 1

STAT 3090 S ECTION 1 L AB A CTIVITY S PRING 2024 c. What is the value of the population mean (average)? Include units with your answer. (4 pts) 8.001 hours of sleep. d. Is the value you listed in part c a parameter or a statistic? Explain. (4 pts) It is a parameter. It describes a populational mean. e. Take one sample of size 9. (4 pts) Under Sampling Options set the Number of samples to 1 and the Sample size to 9. Select Draw Samples . Record below the data values for your sample. Observation Value 1 7.25 2 7 3 8.25 4 6.50 5 7 6 8.25 7 8.25 8 6.50 9 8.75 f. What is the value of your sample mean? Include units. (4 pts) 7.528 hours of sleep. g. Explain why the value calculated in part f is a statistic. (4 pts) It is the average of many different people’s amount of sleep per night. It is a a number describing a sample rather than a population. 2

STAT 3090 S ECTION 1 L AB A CTIVITY S PRING 2024 h. Use the table below to report the mean from 5 samples ( you can draw sample 5 times). (4 pts) Classmate Name: Mean 7.528 7.333 7.722 8.722 8.193 i. Compare your means to that of these five samples. Are the values the same of different? Why? (4 pts) The means are different as it samples 9 different people each time out of a total 18,000 residents. j. The mean you found for your sample is an example of a descriptive statistic. How could you use this value for inference? (4 pts) All the different means are around 8, so you can infer that the overall mean would be close to 8 as well. 2. Stressed Out (21 pts) Because of concerns about employee stress, a large company is conducting a study to compare two programs (tai chi or yoga) that may help employees reduce their stress levels. Tai chi is a 1200-year-old practice, originating in China, that consists of slow, fluid movements. Yoga is a practice, originating in India, that consists of breathing exercises and movements designed to stretch and relax muscles. The company has assembled a group of volunteer employees to participate in the study during the first half of their lunch hour each day for a 10-week period. Each volunteer will be assigned at random to one of the two programs. Volunteers will have their stress levels measured just before the beginning of the program and ten weeks later at the completion of it. The difference in the two stress levels will be recorded. 3

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STAT 3090 S ECTION 1 L AB A CTIVITY S PRING 2024 a. Identify the explanatory and response variables in the following study. Use a sentence or two to explain your choices. (7 pts) Explanatory Variable The explanatory variable is the volunteer group as that s what is being changed. Response Variable The response variable is the stress level of the volunteer group as that is what changes because of the explanatory variable. b. Would this study be considered an experiment or an observational study? Explain. (7 pts) Experimental. The volunteer group is being put through different routines to get data. They are being experimented on rather than just being observed. c. How could you perform this study so that it is the other method from the one you selected in part b? (7 pts) Instead of putting the volunteers into the different programs, simply observe the people that are already involved in the programs and compare their stress levels to the employee’s stress levels. 3. Complete in WebAssign the Section 1 assignment. (39 pts) 4

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